Question: Multiply the following complex numbers: $({-3+3i}) \cdot ({1+5i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-3+3i}) \cdot ({1+5i}) = $ $ ({-3} \cdot {1}) + ({-3} \cdot {5}i) + ({3}i \cdot {1}) + ({3}i \cdot {5}i) $ Then simplify the terms: $ (-3) + (-15i) + (3i) + (15 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -3 + (-15 + 3)i + 15i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -3 + (-15 + 3)i - 15 $ The result is simplified: $ (-3 - 15) + (-12i) = -18-12i $